The impedance budget of the CERN Proton Synchrotron (PS) Serena Persichelli CERN Hadron Synchrotron Collective effects University of Rome La Sapienza serena.persichelli@cern.ch
Why do we study the beam impedances? LHC injectors chain In order to understand the beam dynamics of an accelerator machine that is part of an injector chain, it is important to assess its impedance model: to increase the energy of LHC, the impedances of all injectors have to be well known! The current knowledge of the longitudinal and transverse impedance of the CERN Proton Synchrotron (PS) is established with electromagnetic simulations, theoretical computations and beam-based measurements. Proton Synchrotron: 628 meters long 100 straight sections Injection at 1.4 GeV Extraction at 26 GeV
Transverse impedance: what to expect from the PS Why are we interested in vertical impedance? Example of the PS chambers y y x x Dipolar Quadrupolar Wake integration path Source charge location Vertical impedance is critical respect to horizontal impedance because of the elliptical shape of the PS beam chamber!
How we asses the transverse impedance budget? Tune shift measurements For a Gaussian bunch with rms bunch length σ z, the tune shift Q is proportional to the imaginary part of the transvers effective impedance Z T eee by: Q = 4σ z ββi 0 eee πω 2 II Z 0 Q 0 γm T 0 II Z y = 9. 6 ± 1.0 MΩ/m II Z y = 4. 5 ± 0.1 MΩ/m NB: The differences in the two sets of measurements in the vertical plane can be explained by the coherent space charge effect
Agenda Kickers magnets RF cavities 200 MHz complex 40 and 80 MHz cavities Ferrite loaded: 10 MHz, Finemet cavity Vacuum components Features in the PS beam line Sector valves Comparison with measurements
Agenda Kickers magnets RF cavities cavities 200 MHz complex 40 and 80 MHz cavities Ferrite loaded: 10 MHz, Finemet cavity Vacuum components Features in the PS beam line Sector valves Comparison with measurements
Examples of kickers in the PS Wakefield impedance Kickers are the main source of impedance in the Proton Synchrotron: their presence can explain about the 15% of the vertical impedance measured at 2 GeV!
Agenda Kickers magnets RF cavities 200 MHz complex 40 and 80 MHz cavities Ferrite loaded: 10 MHz, Finemet cavity Vacuum components Features in the PS beam line Sector valves Comparison with measurements
200 MHz cavity: 3D model Wakefield simulations Step 1. Generation of the naked cavity tuned with 4 cylindrical tuners Freq Q R s R/Q 199.9 MHz 6,180 174 kω 28.2 Output coupler oriented of 38º Step 2. Freq Q R s R/Q 199.3 MHz 2,013 55 kω 27.6 9
Modeling of the magnetic output coupler 200 MHz mode magnetic field lines The output coupler has to couple the magnetic field line in order to reduce the Q factor of the resonance: the output coupler is oriented in order to diminish the Q from 6,000 to 1,900 10
200 MHz cavity: 3D model Wakefield simulations Step 3. Input coupler oriented of 180º Freq Q R s R/Q 199.9 MHz 1.094 30 kω 27.4 3 PIN lines for electric coupling Freq Q R s R/Q 199.9 MHz 40 1.03 kω 27.3 Step 4. NB: to extract resonant parameters of the cavity, simulations (with ports) have been performed with the Wakefield solver! 11
Ferrite loaded cavities CST Eigenmode simulations 10 MHz cavity Freq Q R s 3.44 MHz 1.4 2.1 kω New CST release allows to simulate with the Eigenmode solver ferrite loaded cavities! Finemet cavity Freq Q R s 3.39 MHz 0.6? Finemet cavity impedance studies, S. Persichelli, M. Paoluzzi, M. Migliorati, B. Salvant CERN-ACC-NOTE-2013-0033. - 2013 12
RF cavities generation from 2D models Why we need the 3D model Freq Q R s R/Q Freq Q R s R/Q 40.99 MHz 7,027 456 kω 32.5 80.36 MHz 55,538 2.25 MΩ 60 Capacitive coupling 40 MHz 80 MHz 13
40 MHz cavity Electric field RF cavities are not predicted to have a strong impact on the transverse impedance: they can explain less then 1% of the vertical impedance measured at 2 GeV. As an output of the impedance studies, now 3D models are available for the first time for all PS cavities! 14
Agenda Kickers magnets RF cavities cavities 200 MHz complex 40 and 80 MHz cavities Ferrite loaded: 10 MHz, Finemet cavity Vacuum components Features in the PS beam line Sector valves Comparison with measurements
Vacuum equipments in the beam line Wakefield simulations Vacuum equipment and features in the Proton Synchrotron beam line like pumps, valves, bellows, flanges, steps and misalignments are included in the model as distributed elements. Section 43 Vacuum pump Bellow Flange Pumps 100 Sector valves 11 Flanges 259 Bellows ~200 Steps ~60 Misalignments 3
Vacuum equipment: sector valves Wakefield simulations Even if the impedance of the single element is small, the sum of many distributed elements explain about the 5% of the vertical impedance measured at 2 GeV.
Agenda Kickers magnets RF cavities cavities 200 MHz complex 40 and 80 MHz cavities Ferrite loaded: 10 MHz, Finemet cavity Vacuum components Features in the PS beam line Sector valves Comparison with measurements
Transverse impedance budget from simulation Current total transverse impedance Measured value at 2 GeV The purpose of simulation studies is to reach the measured value adding the impedances of single machine elements. Till now, about the 60-70% of the impedance measured at 2GeV, has been explained. The study is ongoing: several elements (wire scanners, pickups, septa, flanges) are going to be added to the current budget. 19
Conclusions The imaginary part of the effective transverse impedance of the CERN Proton Synchrotron has been evaluated by tune shift measurements at different energies The transverse effective impedance has been also evaluated with CST Particle Studio and Microwave Studio simulations: from this budget we are still missing about 30-40% on the vertical plane. A reasonable agreement between measurements and impedance budget has already been obtained on the longitudinal plane. There are still many others elements to be added to the current impedance budget: the study is ongoing!